Experiments in Fluids

, 59:31 | Cite as

Three-dimensional particle tracking velocimetry algorithm based on tetrahedron vote

  • Yutong Cui
  • Yang Zhang
  • Pan Jia
  • Yuan Wang
  • Jingcong Huang
  • Junlei Cui
  • Wing T. Lai
Research Article
  • 156 Downloads

Abstract

A particle tracking velocimetry algorithm based on tetrahedron vote, which is named TV-PTV, is proposed to overcome the limited selection problem of effective algorithms for 3D flow visualisation. In this new cluster-matching algorithm, tetrahedrons produced by the Delaunay tessellation are used as the basic units for inter-frame matching, which results in a simple algorithmic structure of only two independent preset parameters. Test results obtained using the synthetic test image data from the Visualisation Society of Japan show that TV-PTV presents accuracy comparable to that of the classical algorithm based on new relaxation method (NRX). Compared with NRX, TV-PTV possesses a smaller number of loops in programming and thus a shorter computing time, especially for large particle displacements and high particle concentration. TV-PTV is confirmed practically effective using an actual 3D wake flow.

List of symbols

Symbols

A, B, C, D, E, F

Parameters in NRX

A

Angle characteristic parameter of tetrahedron

C

Characteristic matrix of tetrahedron

Dij

Difference between reference tetrahedrons i and j

dmax

Maximum inter-frame particle displacement

Gi

Set of reference tetrahedrons of n

Gj

Set of reference tetrahedrons of m

i

Reference tetrahedron of n

j

Reference tetrahedron of m

L

Edge characteristic parameter of tetrahedron

m

Candidate particle for n in the second frame

n

Particle in the first frame

Ni

Number of reference tetrahedrons of n

Nj

Number of reference tetrahedrons of m

Nm

Number of candidates for n

Nn

Number of particles in the first frame

Nnr

Number of reference particles of n (in NRX)

Nnrc

Number of candidates for a reference particle of n (in NRX)

Nite

Number of iteration loops for NRX

Nmatch

Number of correctly matched particle pairs by PTV

Nmiss

Number of correctly missed particles by PTV

NNRX

Total number of loops in the programming of NRX

NTV

Total number of loops in the programming of TV-PTV

O

Origin in the Cartesian coordinate system

P

Vertex of tetrahedron

R

Radius of the inscribed sphere of the cubic flow field

Rn

Interrogation radius to enclose reference particles (in NRX)

Rs

Interrogation radius to enclose candidate particles

Vm

Total number of votes that m receives from n

Vim

Number of votes that m receives from i

V*

Average vote rate of tetrahedrons

X

Coordinate vector of particle

x

Stream-wise dimension

y

Span-wise dimension

z

Vertical dimension

Greek characters

α

Tetrahedron difference parameter

β

Tetrahedron vote parameter

ζ

Error rate of PTV

η

Accuracy of PTV

Notes

Acknowledgements

This work is funded by National Natural Science Foundation of China (11402190) and China Postdoctoral Science Foundation (2014M552443). Pan Jia is supported by the project LabEx PALM PoPS.

References

  1. Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluids 39(2):159–169CrossRefGoogle Scholar
  2. Baek SJ, Lee SJ (1996) A new two-frame particle tracking algorithm using match probability. Exp Fluids 22(1):23–32MathSciNetCrossRefGoogle Scholar
  3. Bajpayee A, Techet AH (2013) 3D particle tracking velocimetry (PTV) using high speed light field imaging. In: PIV13 10th International Symposium on Particle Image Velocimetry, Delft, The NetherlandsGoogle Scholar
  4. Barnard ST, Thompson WB (1980) Disparity analysis of images. IEEE Trans Pattern Anal Mach Intell 4:333–340CrossRefGoogle Scholar
  5. Brevis W, Nino Y, Jirka GH (2011) Integrating cross-correlation and relaxation algorithms for particle tracking velocimetry. Exp Fluids 50(1):135–147CrossRefGoogle Scholar
  6. Cardwell ND, Vlachos PP, Thole KA (2011) A multi-parametric particle-pairing algorithm for particle tracking in single and multiphase flows. Meas Sci Technol 22(10):105406CrossRefGoogle Scholar
  7. Elsinga GE, Scarano F, Wieneke B, Van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41:933–947CrossRefGoogle Scholar
  8. Fuchs T, Hain R, Kahler CJ (2016) Double-frame 3D-PTV using a tomographic predictor. Exp Fluids 57:174CrossRefGoogle Scholar
  9. Hill D, Troolin D, Walters G, Lai W, Sharp K (2008) Volumetric 3-component velocimetry (v3v) measurements of the turbulent flow in stirred tank reactors. In: Proceedings of the 14th international symposium on applications of laser techniques to fluid mechanics. Lisbon, PortugalGoogle Scholar
  10. Ishikawa M, Murai Y, Wada A, Iguchi M, Okamoto K, Yamamoto F (2000) A novel algorithm for particle tracking velocimetry using the velocity gradient tensor. Exp Fluids 29:519–531CrossRefGoogle Scholar
  11. Jia P, Wang Y, Zhang Y (2013) Improvement in the independence of relaxation method-based particle tracking velocimetry. Meas Sci Technol 24:055301CrossRefGoogle Scholar
  12. Jia P, Wang Y, Zhang Y, Yang B (2015) Relaxation algorithm-based PTV with dual calculation method and its application in addressing particle saltation. J Vis 18(1):71–81CrossRefGoogle Scholar
  13. Knaak M, Rothlubbers C, Orglmeister R (1997) A Hopfield neural network for flow field computation based on particle image velocimetry/particle tracking velocimetry image sequences. In: Proceedings of the IEEE international conference on neural networks, pp 48–52Google Scholar
  14. Labonte G (1999) A new neural network for particle tracking velocimetry. Exp Fluids 26(4):340–346CrossRefGoogle Scholar
  15. Maas HG, Gruen A, Papantoniou D (1993) Particle tracking velocimetry in three-dimensional flows. Part I: photogrammetric determination of particle coordinates. Exp Fluids 15:133–146CrossRefGoogle Scholar
  16. Malik NA, Dracos T, Papantoniou DA (1993) Particle tracking velocimetry in three-dimensional flows. Part II: particle tracking. Exp Fluids 15:279–294CrossRefGoogle Scholar
  17. Mikheev A, Zubtsov V (2008) Enhanced Particle Tracking Velocimetry (EPTV) with a combined two-component pair-matching algorithm. Meas Sci Technol 19(085401):085401CrossRefGoogle Scholar
  18. Nishino K, Kasagi N, Hirata M (1989) Three-dimensional particle tracking velocimetry based on automated digital image processing. Trans ASME J Fluid Eng 111:384–390CrossRefGoogle Scholar
  19. Novara M, Scarano F (2013) A particle-tracking approach for accurate material derivative measurements with tomographic PIV. Exp Fluids 54:1584CrossRefGoogle Scholar
  20. Novara M, Schanz D, Reuther N, Kahler CJ, Schroder A (2016) Lagrangian 3D particle tracking in high-speed flows: shake-The-Box for multi-pulse systems. Exp Fluids 57(8):1–20CrossRefGoogle Scholar
  21. Ohmi K, Li H (2000) Particle tracking velocimetry with new algorithms. Meas Sci Technol 11(6):603–616CrossRefGoogle Scholar
  22. Ohmi K, Panday SP (2009) Particle tracking velocimetry using the genetic algorithm. J Vis 12(3):217–232CrossRefGoogle Scholar
  23. Ohmi K, Panday SP, Sapkota A (2010) Particle tracking velocimetry with an ant colony optimization algorithm. Exp Fluids 48(4):589–605CrossRefGoogle Scholar
  24. Okamoto K, Hassan YA, Schmidl WD (1995) New tracking algorithm for particle image velocimetry. Exp Fluids 19(5):342–347CrossRefGoogle Scholar
  25. Okamoto K, Nishio S, Kobayashi T, Saga T, Takehara K (2000) Evaluation of the 3d-PIV standard images (PIV-STD project). J Vis 3(2):115–123CrossRefGoogle Scholar
  26. Pereira F, Stuer H, Graff E, Gharib M (2006) Two-frame 3D particle tracking. Meas Sci Technol 17:1680–1692CrossRefGoogle Scholar
  27. Ruhnau P, Guetter C, Putze T, Schnoerr C (2005) A variational approach for Particle Tracking Velocimetry. Meas Sci Technol 16:1449–1458CrossRefGoogle Scholar
  28. Schanz D, Schröder A, Gesemann S (2016) Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57:70CrossRefGoogle Scholar
  29. Schröder A, Geisler R, Staak K, Wieneke B, Elsinga G, Scarano F, Henning A (2011) Lagrangian and Eulerian views into a turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids 50:1071–1091CrossRefGoogle Scholar
  30. Si H (2015) TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans Math 41(2):11. https://dl.acm.org/citation.cfm?id=2629697
  31. Song X, Yamamoto F, Iguchi M, Murai Y (1999) New tracking algorithm of PIV and removal of spurious vectors using Delaunay tessellation. Exp Fluids 26:371–380CrossRefGoogle Scholar
  32. Takehara K, Adrian RJ, Etoh GT, Christensen KT (2001) A Kalman tracker for super-resolution PIV. Exp Fluids 29:S34-S41Google Scholar
  33. Troolin DR, Longmire EK (2010) Volumetric velocity measurements of vortex rings from inclined exits. Exp Fluids 48:409–420CrossRefGoogle Scholar
  34. Uemura T, Yamamoto F, Ohmi K (1989) A high-speed algorithm of image analysis for real time measurement of a two-dimensional velocity distribution. Flow Vis ASME FED 85:129–134Google Scholar
  35. Westerweel J, Elsinga GE, Adrian R (2013) Particle Image Velocimetry for Complex and Turbulent Flows. Annu Rev Fluid Mech 45:409–436MathSciNetCrossRefMATHGoogle Scholar
  36. Zhang W, Wang Y, Lee SJ (2008) Simultaneous PIV and PTV measurements of wind and sand particle velocities. Exp Fluids 45(2):241–256CrossRefGoogle Scholar
  37. Zhang Y, Wang Y, Jia P (2014) Improving the Delaunay tessellation particle tracking algorithm in the three-dimensional field. Meas 49:1–14CrossRefGoogle Scholar
  38. Zhang Y, Wang Y, Yang B, He WB (2015) A particle tracking velocimetry algorithm based on the Voronoi diagram. Meas Sci Technol 26(7):075302CrossRefGoogle Scholar
  39. Zhang Y, Wang Y, Yang B, Jia P (2016) Measurement of sand creep on a flat sand bed using a high-speed digital camera: Mesoscopic features of creeping grains. Sedimentology 63(3):629–644CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yutong Cui
    • 1
  • Yang Zhang
    • 1
  • Pan Jia
    • 2
  • Yuan Wang
    • 1
  • Jingcong Huang
    • 1
  • Junlei Cui
    • 3
  • Wing T. Lai
    • 3
  1. 1.Department of Fluid Machinery and EngineeringXi’an Jiaotong UniversityXi’anChina
  2. 2.Laboratoire de Physique des Solides (LPS, UMR 8502)CNRS, Univ. Paris-Sud, Univ. Paris-SaclayOrsayFrance
  3. 3.TSI IncorporatedShoreviewUSA

Personalised recommendations